What is Norton’s Theorem?

What is Norton’s Theorem? 

Norton’s theorem is a method for simplifying a two terminal linear circuit to an
equivalent circuit with only a current source in parallel with a resistor. This basic difference
between Thevenin’s Theorem and Norton’s theorem is that, Norton’s theorem results in an
equivalent source in parallel with an equivalent resistance. The equivalent current source is
designated IN, and the equivalent resistance is designated RN. To apply Norton’s theorem, you
must know how to find the two quantities IN and RN.

Statement:

Norton's theorem states that any two terminal network can be replaced by a single
current source IN in parallel with a single resistance RN.

Procedure:

i) Remove the load resistance RL and put a short circuit across terminals.
ii) Find the short circuit current (IN or ISc)
iii) Find the equivalent resistance RN as seen from open circuited terminals by replacing
the voltage source by its internal resistance.
iv) Draw the Norton’s equivalent circuit by a current ISC in series with the equivalent
resistance Rth or RN
v) Find the current through RL by applying current divider rule.

       IN x RN

IL =--------------
        RN + RL

Explanation: 

Step 1: Remove the Load Resistor (RL) and Short circuit its terminals.

Step 2: Find Short Circuit Current or Norton’s Current (ISC or IN)
ISC or IN = Current through branch A and B
ISC or IN = I3

                                                               R2 x R3
Equivalent Resistance Req = R1 + (----------------)
                                                               R2 + R3

                      E
Current I1 =------
                     Req

Current through Shorted path(ISCor IN) = I3

                          I1 x R2
So, ISCor IN =---------------
                          R2 + R3

Step 3: Find RN (Equivalent Resistance between Terminal A and B)

          R1 x R2
R12 =--------------
          R1 + R2

RN = R12 + R3

Step 4: Draw Norton’s equivalent circuit

Step 5: Find the Load Current (IL):

       IN x RN
IL =-------------
       RN + RL